Service Battery, what does this mean

I think Apple-approved batteries (i.e. the real deal) are the best ones to go with, as batteries from 3rd parties might not work as well or they could actually damage your computer. However I have heard of some people having great experiences with 3rd party batteries, so maybe it depends on the brand.

Rechargeable batteries only last so long before they loose any capacity to hold a charge (the battery's useful life depends on how well you cared for it i.e. calibration etc).

My MBP sometimes comes up with the service battery message when I click on the battery in the menu bar (3 years old). I have found that it does it only when I'm doing something intensive like watching a movie, playing a game or have many programs open at once and the power is being drained unusually fast. Once it is back to regular use the message goes away.

As far as a replacement, I would never trust a battery that didn't come from Apple.

This should answer most, if not all, of your battery questions: Apple Notebook Battery FAQ